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Asset Pricing, the Fama-French Factor Model and the Implications of Quantile Regression Analysis

In traditional tests of asset pricing theory Ordinary Least Squares (OLS) regression methods are used in empirical tests of factor models, which implies a focus on the means of the distributions of covariates. The work of Koenker and Basset (1982) and Koenker (2005) provides an alternative via Quantile regression featuring inference about conditional quantile functions. This study empirically examines the behaviour of the three risk factors from Fama-French Three Factor model of stock returns, beyond the mean of the distribution, by using quantile regressions and a US data set. The study not only shows that the factor models does not necessarily follow a linear relationship but also shows that the traditional method of OLS become less effective when it comes to analysing the extremes within a distribution, which is often of key interest to investors and risk managers.